Only the usual axioms of set theory are needed to prove the existence of a Baire space whose square is not a Baire space. Assuming the continuum hypothesis (CH), Oxtoby [9] constructed a Baire space whose square is not Baire. We will show in this paper that the assumption of CH is unnecessary. Such results are greatly enhanced by Krom [5], who showed that if there is such an example, then there...

In this paper, we prove triple fixed point theorems in partially ordered metric spaces depended on another function. The presented results generalize the theorem of Berinde and Borcut [Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74(15) (2011) 4889–4897]. Also, we state some examples showing that our results are effective.

The purpose of this paper is to prove some coupled fixed point theorems for mapping having the mixed monotone property in partially ordered metric sapces which are generalization of the main results of Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal.TMA 65(2006) 1379 1393]. We support our resul...